Question: Ashley is 14 years younger than Ben. For the last 3 years, Ben and Ashley have been going to the same school. Seventeen years ago, Ben was 3 times older than Ashley. How old is Ben now?
Answer: We can use the given information to write down two equations that describe the ages of Ben and Ashley. Let Ben's current age be $b$ and Ashley's current age be $a$ The information in the first sentence can be expressed in the following equation: $b = a + 14$ Seventeen years ago, Ben was $b - 17$ years old, and Ashley was $a - 17$ years old. The information in the second sentence can be expressed in the following equation: $b - 17 = 3(a - 17)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $b$ , it might be easiest to solve our first equation for $a$ and substitute it into our second equation. Solving our first equation for $a$ , we get: $a = b - 14$ . Substituting this into our second equation, we get the equation: $b - 17 = 3($ $(b - 14)$ $ -$ $ 17)$ which combines the information about $b$ from both of our original equations. Simplifying the right side of this equation, we get: $b - 17 = 3b - 93$ Solving for $b$ , we get: $2 b = 76$ $b = 38$.